Question: $-4ef - 8eg + 5e + 1 = -8f + 9$ Solve for $e$.
Answer: Combine constant terms on the right. $-4ef - 8eg + 5e + {1} = -8f + {9}$ $-4ef - 8eg + 5e = -8f + {8}$ Notice that all the terms on the left-hand side of the equation have $e$ in them. $-4{e}f - 8{e}g + 5{e} = -8f + 8$ Factor out the $e$ ${e} \cdot \left( -4f - 8g + 5 \right) = -8f + 8$ Isolate the $e$ $e \cdot \left( -{4f - 8g + 5} \right) = -8f + 8$ $e = \dfrac{ -8f + 8 }{ -{4f - 8g + 5} }$ We can simplify this by multiplying the top and bottom by $-1$. $e= \dfrac{8f - 8}{4f + 8g - 5}$